Question 1

Suppose that   . Find the following limit. ​   ​

Accepted Answer

A)  -5 
B)  -55 
C)  55 
D)  -11c 
E)  -11 
A)  -5 
B)  -55 
C)  55 
D)  -11c 
E)  -11

Question 2

A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   where x is the distance between the base of the ladder and the house. Find the limit of r as   . ​   ​

Accepted Answer

A)    
B)  50 
C)  0 
D)    
E)  25 
A)    
B)  50 
C)  0 
D)    
E)  25

Question 3

A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places. ​

Accepted Answer

A)  0.9945 inch 
B)  1.5787 inches 
C)  0.9918 inch 
D)  1.9835 inches 
E)  1.7988 inches 
A)  0.9945 inch 
B)  1.5787 inches 
C)  0.9918 inch 
D)  1.9835 inches 
E)  1.7988 inches

Question 4

Find all the vertical asymptotes (if any) of the graph of the function   . ​

Accepted Answer

A)  x = -2 
B)  x= 8 
C)  x= 2 
D)  x= 2, -2 
E)  no vertical asymptotes 
A)  x = -2 
B)  x= 8 
C)  x= 2 
D)  x= 2, -2 
E)  no vertical asymptotes

Question 5

Find the lmit. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Suppose that . Find the following limit.

A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of where x is the distance between the base of the ladder and the house. Find the limit of r as .

A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places.

Find all the vertical asymptotes (if any) of the graph of the function .

Find the lmit.

Preparation for Calculus

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 2: Limits and Their Properties

Suppose that . Find the following limit. ​ ​

A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of where x is the distance between the base of the ladder and the house. Find the limit of r as . ​ ​